A300035 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 5, 1, 1, 12, 12, 1, 1, 37, 22, 37, 1, 1, 104, 81, 81, 104, 1, 1, 301, 307, 427, 307, 301, 1, 1, 864, 1201, 2338, 2338, 1201, 864, 1, 1, 2485, 5066, 13458, 21811, 13458, 5066, 2485, 1, 1, 7144, 21292, 84948, 204034, 204034, 84948, 21292, 7144, 1, 1, 20541

Offset

1,5

Comments

Table starts

.1....1.....1.......1.........1...........1............1..............1

.1....5....12......37.......104.........301..........864...........2485

.1...12....22......81.......307........1201.........5066..........21292

.1...37....81.....427......2338.......13458........84948.........543741

.1..104...307....2338.....21811......204034......2004660.......19807948

.1..301..1201...13458....204034.....3126013.....49405101......783633192

.1..864..5066...84948...2004660....49405101...1240303182....31113970216

.1.2485.21292..543741..19807948...783633192..31113970216..1230133478378

.1.7144.90443.3534493.196822255.12536955677.788871054393.49254153618728

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = 5*a(n-2) +8*a(n-3) +4*a(n-4)

k=3: [order 19] for n>20

k=4: [order 66] for n>68

Example

Some solutions for n=5 k=4
..0..0..1..1. .0..0..1..0. .0..0..0..0. .0..0..1..1. .0..0..1..0
..1..0..0..1. .0..0..1..1. .1..0..1..0. .0..1..1..0. .0..1..1..1
..1..1..1..1. .1..0..1..1. .1..1..0..1. .1..0..0..0. .1..1..0..0
..0..0..0..0. .1..1..0..0. .0..0..1..0. .0..1..1..0. .0..0..1..0
..1..0..0..1. .0..1..0..0. .1..0..0..0. .0..0..1..1. .1..0..1..1

Crossrefs

Column 2 is A297909.

Column 3 is A299216.

Column 4 is A299217.

Sequence in context: A298508 A298328 A299221 * A130227 A114123 A324009

Adjacent sequences: A300032 A300033 A300034 * A300036 A300037 A300038

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 23 2018

Status

approved